Abstract
We construct explicit universal entire curves \(h: {\mathbb {C}}\rightarrow {\mathbb {C}}{\mathbb {P}}^n\) whose Nevanlinna characteristic functions grow slower than any preassigned transcendental growth rate. Moreover, we can make h to be hypercyclic for translation operations along any given countable directions.
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Acknowledgements
Xie is partially supported by National Key R &D Program of China Grant No. 2021YFA1003100 and NSFC Grant No. 12288201. Chen is supported in part by the Labex CEMPI (ANR-11-LABX-0007-01), the project QuaSiDy (ANR-21-CE40-0016) and China Postdoctoral Science Foundation (2023M733690). Huynh is funded by University of Education, Hue University under Grant Number NCM. T.22- 02. We thank Bin Guo (UCAS) for pointing out the reference [4]. We are grateful to the referee for nice suggestions.
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Chen, Z., Huynh, D.T. & Xie, SY. Universal Entire Curves in Projective Spaces with Slow Growth. J Geom Anal 33, 308 (2023). https://doi.org/10.1007/s12220-023-01368-w
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DOI: https://doi.org/10.1007/s12220-023-01368-w
Keywords
- Universality
- Entire curves
- Hypercyclicity
- Nevanlinna characteristic functions
- Nevanlinna theory
- Rational approximations